So far, the concept of neighborhood for a point has been defined and used as one of the fundamental concepts in determining the limits of functions and, in general, in differential calculus. This concept has been defined for a continuous interval of real numbers. However, a different definition of neighborhood has also been presented using the set theory for a finite number of discrete and specific members, which includes simple and elementary concepts. Application of this new type of neighborhood has been reported to optimizing the ultimate stope limits in underground mining. In this paper, the initial concept of discrete neighborhood has been extended for members of sets, defined and detailed in one-, two-, and three-dimensional spaces, which are referred to, here, as geosets or spatial sets. In this regard, a number of concepts was first defined including linking factors, neighbors, neighborhoods and order (or distance) of neighborhood. Definable neighborhoods, feasible neighborhoods, infeasible neighborhoods and neighborhood space were determined. Neighborhood numbers were also specified and identified. It was found that definition of geosets as a new category in the set theory and developing the neighborhood concept, as proposed here, may provide a platform to extend application of the set theory to new engineering problems.